29,007 research outputs found
Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production
I present results for two-loop soft anomalous dimensions for heavy quark
production which control soft-gluon resummation at
next-to-next-to-leading-logarithm (NNLL) accuracy. I derive an explicit
expression for the exact result and study it numerically for top quark
production via e+ e- -> t tbar, and I construct a surprisingly simple but very
accurate approximation. I show that the two-loop soft anomalous dimensions with
massive quarks display a simple proportionality relation to the one-loop result
only in the limit of vanishing quark mass. I also discuss the extension of the
calculation to single top and top pair production in hadron colliders.Comment: 10 pages, 6 figures; improved form of the analytical result; equation
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Beyond Sperner's lemma
The present paper is devoted to a recent beautiful and ingenious proof of
Brouwer's fixed point theorem due to mathematical economists H. Petri and M.
Voorneveld. The heart of this proof is an analogue of Sperner's lemma motivated
by Shapley-Scarf model of markets of agents with preferences over indivisible
goods.
The goal of the paper is to present a relatively abstract version of
Petri-Voorneveld proof which makes transparent both its similarities and its
differences with the classical proof based on Sperner's lemma and a well known
Knaster-Kuratowski-Mazurkiewich argument.Comment: 9 page
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